Name: Reynolds Number
Uploaded: 2019-07-19
Duration: 5 min 6 s
Description: Before analysing anything, the first step is to find out whether the flow is laminar or turbulent. There is just the right indicator that tells us this. Watc...

Question

What is critical velocity of fluid? From dimensional analysis find an expression fur the critical velocity. Define Reynold's number and state its significance.

Accepted Answer

Critical velocity is the greatest velocity with which a fluid can flow through a given conduit without becoming turbulent.

$Critical velocity (V C) = \frac{R e η}{ρ r} where R e = Reynolds number η = coefficient of viscosity ρ = density of fluid r = r a d i u s o f t u b e . Dimensional Formula of Reynolds number (R e) = M^{0} L^{0} T^{0} Dimensional Formula of coefficient of viscosity (η) = M^{1} L^{- 1} T^{- 1} Dimensional Formula of Density of fluid (ρ) = M^{1} L^{- 3} T^{0} Dimensional Formula of radius (r) = M^{0} L^{1} T^{0} Putting these values in above equation we get, V C = \frac{[M^{0} L^{0} T^{0}] [M^{1} L^{- 1} T - 1]}{[M^{1} L^{- 3} T^{0}] [M^{0} L^{1} T^{0}]} Dimensional Formula of Critical velocity(VC) = M^{0} L^{1} T^{- 1}$

The Reynolds number is the ratio of inertial forces to viscous forces. The Reynolds number is a dimensionless number used to categorise the fluids systems in which the effect of viscosity is important in controlling the velocities or the flow pattern of a fluid.

What is critical velocity of fluid? From dimensional analysis find an expression fur the critical velocity. Define Reynold's number and state its significance.

Important Questions on Fluid Dynamics

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